Timeline for Dixmier's lemma as a generalisation of Schur's first lemma
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 15, 2023 at 7:23 | comment | added | Michael_1812 | @UriBader I understand that in Hilbert spaces $M=c$ Id even in uncountable dimensions, because of the property that the spectrum of any bounded operator is non-empty there. Could you please give me a reference on this property? Preferably, some simple introductory text available to a layman. | |
| Sep 14, 2019 at 14:10 | comment | added | Michael_1812 | @UriBader Thanks again. I am glad that my question has attracted attention, and hope that, owing to your detailed answer, more people (including bona fide mathematicians) benefit from this conversation. | |
| Sep 14, 2019 at 7:03 | comment | added | Uri Bader | Let me also add that I put my answer there as a service to the community, trying to explain a framework in which the question and answer make sense which is more general than the one you originally intended. I had in mind a potential reader whose education and background are similar to mine. I didn't think of physicists folks like yourself. I apologize for that unintentional bias. | |
| Sep 14, 2019 at 7:03 | comment | added | Uri Bader | Michael, I meant to say a field $k$ and $D$ meant to denote a generic $k$-division algebra. Using $k$ and $D$ in these context are to some (but apparently not to all) as hintful as using $\epsilon$ and $N$ when regarding the convergence of a sequence. The use of the letter $k$ for a field is maybe more standard than the use of $F$. I believe it comes from the German term "Körper" introduced by Dedekind. The spelling mistake is mine alone. Also, I should have explained better what $D$ meant - I will edit my answer. | |
| Sep 13, 2019 at 21:39 | comment | added | Michael_1812 | @UriBader You probably wanted to say not "filed k" but "field f", right? | |
| Sep 13, 2019 at 17:07 | comment | added | Michael_1812 | @UriBader Also, what is D in your answer? | |
| Sep 13, 2019 at 16:26 | comment | added | Michael_1812 | @UriBader Thank you for your comment! You are certainly right: less than continuum would be more exact. The problem is not with your answer, but with us physicists who lack the ability to understand the language of pure math. In the beginning of your answer, you say: "we fix a filed k". What is "filed k"? | |
| Sep 13, 2019 at 8:16 | comment | added | Uri Bader | Allowing myself a bit of nitpicking, you should not write "for countable dimensions only", but "for dimension less than continuum only", as explained in my answer. Moreover, your answer here is essentially the content of my last line (in parentheses). | |
| Sep 12, 2019 at 22:07 | history | answered | Michael_1812 | CC BY-SA 4.0 |